First the scalp, now the songbook. Manchester City claimed primacy from their erstwhile oppressors by storming Old Trafford on Sunday; here, they enshrined the shift of power in mocking memory. "We're Man City," they crooned, to the tune of the Beach Boys' "Sloop John B" so beloved of Manchester United. "We'll score when we want."

And as much as they want, as fast as they want, against who they want. Three goals in three minutes and 42 seconds just before half-time quieted Molineux, crushed Wolves and sent Roberto Mancini's second string to the quarter-finals of the Carling Cup. Two further strikes in the second half took City's tally to 11 in two games and 45 in 15 for the season, despite the Italian making wholesale changes to the team which saw off United. They are, put simply, irresistible.

"This is football," said Mancini. "There are times when you score a lot of goals every game and there are times when you just cannot score at all. Every team goes through phases like that."

Few go through patches as purple as this. Even when Nenad Milijas swivelled and smashed Mick McCarthy's team into an early lead, it had a Canutian air about it. Such is the ruthlessness, the relentlessness that Mancini has instilled in this team that it was never really in doubt that, at some point, the light blue tide would break upon the Old Gold shore. City are no great purveyors of beauty, as Barcelona or Arsenal could be held to be. Instead, they provide blitzkrieg.

And so, in the space of 222 seconds, they overwhelmed their hosts. Adam Johnson drilled home from the edge of the area. His sumptuous pass put Samir Nasri through two minutes later, the Frenchman slotting past Dorus De Vries. Then Edin Dzeko bundled home after Luca Scapuzzi, the 20-year-old Italian, saw his effort saved. The game over in the blink of an eye.

There was no ceasefire to the onslaught. Scapuzzi forced his first for the club home immediately after the break, Dzeko converted the Italian's cross on the hour and might have had three more, at the very least. Only Jamie O'Hara's strike, with his first touch, staunched the flow, foiling City's attempts to replicate Sunday's historic result.

And still Mancini – who also denied Mario Balotelli had been involved in a row with one of his coaches after full-time – wants more. "I think Adam Johnson can be one of the best wingers in Europe," said the City manager, of the midfielder's man-of-the-match display. "But I think he can do more.

"I do not like it when players think they have scored one goal and made one goal and so they can stop. I prefer them to think they want to score another, make another, and still track back to defend. For Wolves' second goal he should have run back. He can still improve this."

Such desire for perfection is what has brought Mancini to the top of the league, at the helm of the most fearsome force in the country, a club that can send out a reserve team – admittedly one of the most expensive ever assembled – and still disassemble top-flight opponents.

It is difficult not to pity the team tasked with stemming their inexorable march at the Etihad Stadium on Saturday. "There's no point going into it with any sort of trepidation," said McCarthy, with typical bluntness. "No point playing that way at all." The mood City are in, there may be no point full stop.